Robust Mean Estimation under Quantization

TL;DR

This paper develops robust mean estimators that operate effectively under quantization constraints and adversarial corruption, achieving near-optimal performance in one-bit and partial quantization scenarios.

Contribution

It introduces new multivariate robust estimators tailored for quantized data, improving robustness and optimality in challenging settings.

Findings

Optimal up to logarithmic factors in one-bit setting

Effective in partial quantization with limited unquantized data

Robust against adversarial corruption

Abstract

We consider the problem of mean estimation under quantization and adversarial corruption. We construct multivariate robust estimators that are optimal up to logarithmic factors in two different settings. The first is a one-bit setting, where each bit depends only on a single sample, and the second is a partial quantization setting, in which the estimator may use a small fraction of unquantized data.